dQ(τ)/dx_{j} = dg(Q_{h(Y)})/dx_{j}

where x_{j} is the j-th covariate with respect to which the marginal effect is to be computed and its name is given in the argument namevec.

The derivative of the quantile function is the the product of two components

dQ(τ)/dx_{j} = dg(η)/dη dη/dx_{j}

The derivative w.r.t. the linear predictor η is calculated symbolically after parsing the object's formula and is evaluated using the object's model frame. The function that parses formulae has a limited scope. It recognizes interactions and basic operators (e.g., log, exp, etc.). Therefore, it is recommended to use simple expressions for the model's formula.

This function can be applied to models of class rqt and rq.counts. Note that marginal effects can be similarly obtained using predict.rqt or predict.rq.counts with argument type = "maref" which, in addition, allows for an optional data frame to be specified via newdata.

Value

a vector for single quantiles or a matrix for multiple quantiles of marginal effects.